Piezo-electric wave filter



. P w. P. MASON 1,974,081

PIEZO ELECTRIC WAVE FILTER Filed March 28, 1933 2 Sheets-Sheet 1 FIG. 2

FIG. 3

II I l' I l FIG. 4 U I a I E0 u I FREQUENCY :5 I t I I I I I I l I 'l lFIG. 5

F IG. 6

c c INVENTOR M! MASON A TTORNEV Sept. 1 8, 1934. w, v so 1,974,081

PIEZO ELECTRIC WAVE FILTER Filed March 28, 1933 2 Sheets-Sheet 2 INVENTOR W P MASON ATTORNEY Patented Sept. 18, 1934 mmsms l 1 i 1,37 i',081

ris'zo nriic r n c Ways .rnxrisrz' This invention relates to broad bandwave filters in which piezoeelectric crystals are .used as":

impedance elements and has for itsmprincipal object'to extend the rangeof transmissionzchar- 5 acteri'sti'cs'that can be obtained with filtersof this type. Another object is to reduce the niimber of crystalsrequired for a desired selectivity;

The electrical impedance of a quartz piezoelectric crystal, as is wellknown, is characterized Ma resonance and an antieresonance atfrequencies very close to each other andby 'a high capacitive reactanceelsewhere. This characteristic makes" it difiicult to combine crystalsin a filter circuit to. obtain .a reasonably :wide transmission band andat the same time toprovide a high attenuation level outside the band.The problem is discussed' in my earlier application, SerialNo/653522filed January 26, 1933, where-' in one arrangement is described forobtaining relatively wide transmission bands by combining crystal of]the filter." With this arrangement, band widths'as 'greatas' 14 percentof the mean 2 frequency .are obtainable without sacrifice of the furtherextension of the bandwidth consistent with a high attenuation levelismade possible L31; and a capacity C31.

by theuse of inductances connectedbothin series with and in shunttoeach' crystal of a filter. Two

separate inductances may be associatedwitheach crystal but in thepreferred formsot .theinven tion the inductances are arranged totormjrans formers through which the crystals 'areicoupled. to the,filteribranches This arrangement has the advantage that in .manyfcasesthe transformer ratios may be adjusted'to permit th'e'us'e of morepractical crystal dimensions than would obtain with directly connectedcrystals. In one form of the inventionthe same crystal is coupledsimultaneously into two branches of the filter network by means of aspecial transformer, there'- by reducing the niunber ofcrystals requiredto a 4 minimum.

As the number of inductance elements asso-I ciated with the crystals ofa filter is increased the v the'line branches, obtained: by substitutingthe effects of energy dissipation in the coil resistances become moreimportant and the advantagesarising from'the substantiallydissipationless character of the piezo-electric crystal tend-tedisappear. In the circuits of the'inve'ntion the re.-

sistance of one of the added inductancesin each capacity. C21. The otherelements are designated-;

ofthezother. partially compensated so, thatzthej to correspond. toFig.1.. Since the electrical 5 branch can be completely compensated andthat ductance L32 and capacity C32.

bination iL, 9G,. representing the-piezo-,elec.tric7r 'p'acity C.

ifilterselectivity is substantially' that of ads tsipationless network;

The invention will be more fully understood' 'from the followingdetailed :description'of repr e-r sentative circuits and from theappendedzdrawes ings, of which:

Fig. 1 shows in schematic form oneembodimentg;

of the invention; 1

Figs. 2 to 6, inclusive, are'diagrams explanatory of the invention;

of the filter of Fig. 1;

Fig. 7 shows a preferred form Fig. 8 is explanatory of the filter ofFig. 7';

Fig. 9 shows amodified form :of'the network of.

Fig. 7, and

Figs. 10 to 12, inclusive, show additional err.-

amples of filters in accordance with the invention.

impedancesconnected betweeninput terminals 1,;-

an inductance in series or, in shunt-with 'ea c'h' Y 2,and-'output-terminals 3, 4;; In" this .andfin subsequent figures onlyone :line impedance and";

one lattice impedance is shown invdetail for the i sake ofz'clarity, theother corresponding branches attenuation level at frequencies remote'from 'the v having identical elements.

"each comp-rise a piezo-electric crystal X1 shunted In accordance withthe presentinvention] by a small capacity C21, preferably an adjustableThe line 'impedances.

The lattice impedances; are of similar construction comprisinga-crystalX2 shunted byan inductance Lzz'and a capacity" C22 and-including theseries combination, of in- The'lcrystals are preferably of quartz,:cut'and; mounted in the rnanne'r described in my-eaflier: co-pendingapplication, Seria11No...65'3,622 'filed impedances correspondaccurately to that of the electrical system of Fig Thisequivalentelectrical impedance comprises a series resonant com- January 26,-1933,'in which'case theirelectricalaf;

prop'ertiesxof, the crystal, shunted by a capacity Co,repr'esentingtheelectrode capacity; which has a minimum value. of about125 times the. c-a-j The complete electrical equivalent of one of"impedance. of Fig. 2 for the crystal; is ShOWIlmv in Fig. 3 inwhichthe'combination' L11, C11, rep

electrodecapacity plus the external shunting resonant.

equivalent contains six elements its reactance will be characterized byfive critical frequencies of finite values, that is, there will be fivefrequencies at which the impedance is resonant or anti- The variation ofthe reactance with frequently is illustrated by curve 10 of Fig. 4, thecritical frequencies being designated ii to is in ascending order. Thereactance of the lattice branches of Fig. 1 will have a similarfrequency characteristic with the same number of critical frequencies.

The general rules for the proportioning of impedances in a symmetricallattice with respect to each other to provide desirable transmissioncharacteristics are described in U. S. Patent 1,828,454 issued October20, 1931 to H. W. Bode and their application to piezo-electric crystalfilters is discussed in my above mentioned co-pending application. Inaccordance with these principles one way of proportioning the latticereactances in Fig. 1 is illustrated by curve 11 of Fig. 4, which showsthe lattice branch reactance characteristic, the critical frequenciesbeing allocated with respect to those of the line branch reactance' toprovide a single transmission band. In this arrangement the latticebranch has resonances coinciding with the anti-resonances of the linebranch at frequencies f2 and f4 and antiresonances coinciding with isand f5. The highest -:resonance occurs at an additional frequency f6 andthe transmission band extends from ii to is.

In my above mentioned co-pending application it is pointed out that infilters of simpler structure it is desirable that the several criticalfrequencies should form a geometric series or should approximatethereto, this type of spacing permitting the attenuation to bemaintained high'at frequencies outside the band. The same rule isapplicable to the present types of filter, abut in many cases it ispreferable to modify the distribution of the frequencies somewhatparticularly in the direction of spacing them closer together towardsthe edge of the band. For the case in. which the critical frequenciesform a. geometric series the proportioning of the impedances is simple.Considering the structure of Fig. 3, the inductance L21 should be madeto resonate with the capacity Czi at the crystal resonance frequency.The combination of the crystal. and the shunt inductance will then havea reactance characteristic of the type represented by curve 12 of Fig.5. This curve exhibits a resonance at frequency is, which is the crystalresonance, and two anti-resonances f2 and I4 spaced geometrically aboveand below is. The separation between the anti-resonance frequencies isdetermined by the ratio of the capacities C11 and Czi and is given bythe formula If the additional elements L31 and C31 are adjusted toresonate also at frequencyfa their reactance will have a frequencycharacteristic of the type illustrated by curve 13 of Fig. 5/ It isclear that the addition of such a reactancewill not disturb theresonance at frequency is or the anti-resonances at f2 and f4, but willsimply introduce additional resonances above and be- 1O Wf2 and f4,which, due to the symmetry of the circuit will likewise'be spacedgeometrically about the frequency is. The proportioning of the crystaland shunt inductance combination thus determines three of the criticalfrequencies of the total impedance and also the ratio of the successivefrequencies. To make the additional critical frequencies fall into theseries, I find that the capacity C31 of the added resonant circuitshould be given the value C 31= ll( +2 73 and the inductance L31proportioned accordingly.

Since the ratio of Cu to 0'21 determines the separation of thefrequencies f4 and f2 it follows that, in the case described, the totalband is controlled by this ratio. For crystals of the preferred type theelectrode capacity has a minimum value about 125 times thepiezo-electric capacity, corresponding to a value of the frequencyinterval 14-12 equal to 9 per cent of is for the case where thefrequencies are in a geometric series. The addition of the externalshunt capacity C21 permits the reduction of this interval as much as maybe desired, thus making possible a band width range from about zero to25 per cent of the mean band frequency. I

In the more general case in which the critical frequencies do not lie ina geometric series the computation of the elements may be carried on asfollows:

The impedance, Z1, of the line branches may be expressed in terms of L31and the critical frequencies as r and the impedance Z2 of the latticebranches as in which w denotes 211' times frequency.

By thedirect application of Fosters reactance theorem, described in theBell System Technical Journal Vol. III, No. 2, April 1924, page 259, the

elements of an impedance of the type shown in.

Fig. 6 may be calculated from the expression for Z1 and a correspondingimpedance for Z2. impedance shown in Fig. 6, while equivalentelectrically to the filter line branch impedance is different from itstructurally since it contains,

two series connected anti-resonant combinations The.

LaCa and LbCb instead of the inductance shunted.

and to have a value Km at the mean frequency of the band given by a IfL31 is made equal to Liz the common value is determined by Equation 6.

For the case in which the critical frequencies form a geometric seriesit will be noted thatthe external capacity C31 of the line branch isapproximately'three times the piezo-electric capacity of the crystal.

is inconveniently small and the inductance L31 is inconveniently great.Alternativelygif C311 and k Since the latter is frequently verysinall itmay be found that the capacity C31 which vary through a wide range ofvalues, reach- L31 are proportioned to'give desirable values of thecharacteristic impedance it may be found that the crystal capacities aresuch that can-be obtained only With excessively thin crystals. Thesedifficulties are avoided in a modified form of the invention illustratedin Fig. '7 in which the crystals are coupled to the lattice branchesthrough step-down transformers. 1

The line branches in the filter of Fig. "I each comprise a capacity C31in' series with an inductance Lpl to which is coupled a'secondaryinductance LS1; Across the terminals of this in ductance are connectedthe piezo-electric crystal X1 and the band controlling shunt capacityC21. The lattice branches are similar in structure comprising seriescapacity C32 inductance L132 and a secondary system made up ofinductance L52, crystal X2 and capacity C2.

The branches of this filter differ structurall from those of the filterof Fig. 3, but, since they contain the same number of elements and sincetheir reactances'at zero and infinite frequencies are the same asfor thebranches of Fig/.3, the two filters are potentially equivalent. By knownmethods the line branch impedance of the filter of Fig. '7 may betransformed to the type shown in Fig. 8, which comprises the capacityC31, un-. changed in value, a series inductance of value (Lpl- Lsl), andthe. parallel combination of an inductance L5 a capacity C21+ and acrystal of impedance ZX1, where Zxl is the impedance of crystal X1. Thefactor appearing in these values is an impedance transformation ratiohaving the value where M1 is the mutual inductance between inductances L11 and LS1. The resistances of the inductance coils are shown in Fig. 8,the resistance r 11 being that of inductance Lpl and the resistance 1'51being that of inductance L51. The latter appears in series with thecrystal and its shunt capacity, its value being modified in accordancewith the transformation ratio.

Since the impedance shown in Fig. 8 corresponds, except for the locationof the resistances, to the branch impedance of Fig. 1 it follows thatthe design procedures outlined above in connection with that figure canbe applied to the circuit of Fig. 8 and hence to the filter of Fig. 7.The impedance ratio may evidently be made as small as may be desired byproperly proportioning the coupling between the inductances. The effective impedance of the crystal may thus be brought to any desired value;so permitting the capacity C31 and its associated inductance (Lp1 Lsl)to be kept within practical values.

The effects of the coil resistances may now be considered. Theresistances of the series coils Lpl and Lpz may be made equal in whichcase their effects balance each other so that the selectivity of thefilter is not disturbed. Equal series resistances in the four branchesof a symmetrical lattice have the same effect as a resistance of thesame value added in series external to the lattice at each end. That is,the effect is simply that which would arise from a slight change in theresistances of the impedances between which the lattice is connected.The secondary coil resistances cannot be made to balance each othercompletely but they do so partially. Since they appear in the branchimpedances as part of an anti-resonant loop circuit they will produceeffective series resistances ing maximum values. at the anti-resonancefrequencies of the impedance.

'To maintain the sharpness of selectivity characteristio ofdissipationless structures it is desirable principally that theeffective resistance should be negligibly small at the cut-offfrequencies and at frequencies in theattenuation range close thereto. Inthe filters of the types described above two factors help towards therealization of this condition. The first is that the anti-resonancefrequencies lie within the band some distance from the cut-offfrequencies so that the effective resistance at the cut-off frequenciestends to be fairly small-and diminishes in the attenuation ranges. Thesecond factor lies in the proportions of branch impedances due toinherent relationships of the effective capacities of the crystals whichhave .a minimum ratio of about 125., In connectionwith the filter ofFig. 1 it was'pointed out that for geometric spacing of the criticalfrequencies the series capacities C31 and C32 have valuesaboutB timesthe piezoelec+ tric capacity of the crystal. .Since the seriesinductances Lz1-and L32 are, proportioned to resonate with thesecapacities at, the crystal resonance and since theshunt inductances L21and L22 are proportioned to resonate with the total shunt capacities ofthe crystals at the same frequency, it follows that. the seriesinductancesmust be at leastAO times as great as the shunt inductances.This relationship is, of course, accurate only for the case of thegeometric arrangement of the critical frequencies, but it holdssubstantially for most practical filter designs. The effectiveresistances due to, the dissipation in the low inductance shunt coilstherefore appear in series with the very large reactances of the seriescoils and condensers which representqthe dominant part of the totalimpedance outside the band. The effect of the shunt coil dissipationthus becomes negligibly small at frequencies. quite close to thecut-off. From experiment and calculation I have found that theunbalanced effective resistance corresponds to less than 20 per cent ofthe series coil resistance. Since similar relationships are involved inthe filter of Fig. 7 the effects there are of like character andmagnitude.

A modified form of the filter of Fig. '7 is shown schematically in Fig.9, the feature of this network being that instead of having a separatecrystal for each arm of the lattice only two crystals are used one ofwhich is coupled by a double primary transformer to the two linebranches, and the other of which is similarly coupled to the two latticebranches. The designation of the elements in Fig. 9 corresponds to thedesignations in Fig. 7. This circuit has the advantage that, besidesreducing the number of crystals by half, the necessity for balancing theline and the lattice arms to secure symmetry is largely eliminated.

Additional examples of filter networks in accordance with the inventionwhich are obtained by changing the location of the external capacitiesare illustrated by Figs. 10, 11 and 12, the elements being designated tocorrespond to Fig. '7. The filter of Fig. 10 is a band pass filter inwhich the primary coils are tuned by means of shunt condensers ratherthan series condensers. Fig. 11 represents a low pass filter obtained byomitting the series condensers from the line branches of the network ofFig. '7. Fig. 12 illustrates a high pass filter obtained by omitting theshunt tuning condensers from the line branches of the filter of Fig. 10.The capacities in shunt to the crystals are not shown in these figures,but it will be understood that such capacities may be employed asdesired. It will be evident also that these networks may be modified inaccordance with Fig. 9 to reduce the number of crystals.

What is claimed is: l

1. A broad band wave filter comprising a plurality of impedance branchesinterconnecting a pair of input terminals and a pair of outputterminals, said branches having reactances ofdiverse frequencycharacteristics proportioned'with respect to each other to provide asingle transmission band, each of said branches including apiezo-electric crystal, an inductance in parallel with said crystal, anda second inductance contributing a reactance. effectively in series withsaid parallel combination.

2. A broad band wave filter comprising a plurality of impedance branchesinterconnecting a pair of input terminals and a pair of outputterminals, said; branches having reactances of diverse frequencycharacteristics proportioned with respect to each other to provide asingle transmission band, each of said branches including a primaryinductance, a secondary inductance coupled thereto and a piezo-electriccrystal con.- nected in parallel with said secondary inductance.

3. A broad band wave filter comprising two pairs of similar impedancebranches connected between input terminals and output terminals to forma symmetrical lattice network, a primary inductance included in each ofsaid branches, secondary inductances coupled to said primaryinductances, and a piezo-electric crystal connected across the terminalsof each of said secondary inductances, the impedances of said crystalscooperating with the reactances of said inductances to provide acontinuous transmission band.

4. A wave filterin accordance with claim 3, in

which the primary inductances are coupled in pairs to singlesecondaryinductances. I 5. A broad-band wave filter comprising a plurality ofimpedance branches interconnecting a pair of input terminals and a pairof output terrality of impedance branches similar in pairs connectedbetween input terminals and output terminals to form a symmetricallattice, a primary inductance and a tuning condenser. therefor includedin each branch, secondary inductances coupled to said primaryinductance, and a piezoelectric crystal connected across the terminalsof each of said secondary inductances, the im-, pedances of saidcrystals co-operating withthe reacta'nces of saidinductanes and saidtuning condensers to provide acontinuous transmission band. V f

'7. A wave. filter in accordance with claim 6 in which the said tuningcondensersare connected in series with the said primary inductances.

8. A Wave filter in accordance with claim 6 in which the said tuningcondensers are connected in parallel with the said primary inductances.

WARREN P; MASON.

lOO

